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Pasco Scientific ME-9429A, Instruction Manual And Experiment Manual

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Pasco Scientific ME-9429A Instruction Manual And Experiment Manual Download Page 15

11

012-05035E

Dynamics Cart Accessory Track Set

Experiment 3: Simple Harmonic Oscillator

EQUIPMENT NEEDED:

– Dynamics Cart with Mass (ME-9430)

– Dynamics Cart Track

– (2) Springs

– Super Pulley with Clamp

– Mass hanger and mass set (ME-9348)

– Stopwatch

– String

– Mass balance (SE-8723)

– Graph paper

Purpose

The purpose is to measure the period of oscillation of a spring and mass system and compare it
to the theoretical value.

Theory

For a mass attached to a spring, the theoretical period of oscillation is given by

T

= 2

π

m

k

where 

T

 is the time for one complete back-and-forth motion, 

m

 is the mass that is oscillating,

and 

k

 is the spring constant.

According to Hooke’s Law, the force exerted by the spring is proportional to the distance the
spring is compressed or stretched, 

F = kx

, where 

k

 is the proportionality constant. Thus the

spring constant can be experimentally determined by applying different forces to stretch the
spring different distances. Then the force is plotted versus distance and the slope of the result-
ing straight line is equal to 

k

.

Procedure

Measurements to Find the Theoretical Period

➀

Use the balance to find the mass of the cart. Record this value at the top of Table 3.1.

➁

Level the track by setting the cart on the track to see which way it rolls. Adjust the leveling
feet at the ends of the track to raise or lower the ends until the cart placed at rest on the track
will not move. Put the pulley with the table clamp at one end of the track.

➂

Set the cart on the track and attach a spring to each end of the cart by inserting the end of the
spring in the hole provided in the cart. Then attach the other ends of the springs to the endstops
(See Figure 3.1).

➃

Attach a string to the end of the cart and hang a mass hanger over the pulley as shown.

➄

Record the equilibrium position in Table 3.1.

➅

Add mass to the mass hanger and record the new position. Repeat this for a total of 5 different
masses, being careful not to over-stretch the springs. Because both springs are acting on the
mass, this method will give the effective spring constant for both springs.

Summary of Contents for ME-9429A

Page 1: ...cessory Track Set 1 2m version CAUTIO N M AG NET AVO ID CO NTACT W IT H CO M PUTERS Model ME 9 435 DYNAMIC S TRACK Instruction Manual and Experiment Guide for the PASCO scientific Model ME 9435A and ME 9429A Includes Teacher s Notes and Typical Experiment Results ...

Page 2: ......

Page 3: ...n of Momentum in Explosions 7 Exp 2 Conservation of Momentum in Collisions 9 Exp 3 Simple Harmonic Oscillator 11 Exp 4 Oscillations on an Incline 15 Exp 5 Springs in Series and Parallel 19 Exp 6 Newton s Second Law 22 Exp 7 Newton s Second Law II 23 Exp 8 Acceleration down an Incline 25 Exp 9 Conservation of Energy 29 Additional Experiments 33 Teacher s Guide 35 Technical Support Inside Back Cover...

Page 4: ...o prevent damage and shipped postage or freight prepaid Damage caused by improper packing of the equipment for return ship ment will not be covered by the warranty Shipping costs for returning the equipment after repair will be paid by PASCO scientific Copyright Warranty and Equipment Return Please Feel free to duplicate this manual subject to the copyright restrictions below Equipment Return Shou...

Page 5: ...nd accurate alignment with the lowest possible friction and it accomodates most linear motion experiments Features include Length is adequate for standard experiments and limited lab and table space Low friction wheel slots keep the carts aligned even after a collision Mounted to a standard lab rod the track adjusts to any angle for inclined plane experiments Durable construction with built in End...

Page 6: ...ck Magnet Bumper Kit includes 2 magnets with storage tube Pivot Clamp for use with the Base and Support Rod ME 9355 Label CAUTION MAGNET Additional Equipment Required for ME 9458 Dynamics Cart with Mass ME 9430 Specific experiment requirements Thread Mass Set Super Pulley with Clamp Base and Support Rod Metric Ruler Stopwatch Mass balance Wooden or metal block Graph paper Additional Equipment Reco...

Page 7: ...mbly consists of a foam pad attached to a neodymium magnet The neody mium magnets are extremely strong Though only the south end of the magnet is exposed they can still be a hazard When opposite poles are brought close to each other they will accelerate rapidly and can pinch fingers or be easily chipped They can also erase computer disks and distort computer monitors and television sets Replace th...

Page 8: ...ference Align the square nut within the groove on the de sired side of the Dynamics Cart Track as shown Locate and adjust the End Stop to the desired posi tion and tighten the thumb screw to secure When storing the End Stop when it is not on the track remember that it has two strong magnets in it Keep the End Stop away from computers Attaching Adjustable End Stop to Track The Friction Block is a w...

Page 9: ...lley with Clamp 1ea ME 9448A Friction Block 1ea 003 04708 Label Magnet Caution 1ea 646 04445 Spring 3ea 632 04978 Pivot Clamp Assembly 003 05019 Pivot clamp 1ea 648 04654 Long thumb screw 1ea 610 183 620 047 Short thumb screw 1ea 610 181 620 067 Washer 615 184 Square nut 1ea 614 054 Adjustable End Stop 1ea 003 04989 Fixed End Stop 1ea 003 05018 ...

Page 10: ...6 Dynamics Cart Accessory Track Set 012 05035E Notes ...

Page 11: ...esulting total mo mentum of the system is still zero p m1v1 m2v2 0 Therefore the ratio of the final speeds of the carts is equal to the ratio of the masses of the carts v1 v2 m2 m2 To simplify this experiment the starting point for the carts at rest is chosen so that the two carts will reach the end of the track simultaneously The speed which is the distance divided by the time can be determined b...

Page 12: ... other CASE 3 CARTS OF UNEQUAL MASS Put two mass bars in one cart none in the other CASE 4 CARTS OF UNEQUAL MASS Put two mass bars in one cart one mass bar in the other Table 1 1 Data Analysis For each of the cases calculate the distances traveled from the starting position to the end of the track Record the result in Table 1 1 Calculate the ratio of the distances traveled and record in the table ...

Page 13: ...is is accomplished with the hook and pile tabs on the end caps of the carts Procedure Level the track by setting a cart on the track to see which way it rolls Adjust the leveling feet at the end of the track to raise or lower that end until a cart placed at rest on the track will not move Draw two diagrams one for before the collision and one for after the collision for each of the following cases...

Page 14: ...rack Give the first cart a slow velocity and the second cart a faster velocity so that the second cart catches the first cart Do this for both cases with the 1M cart first and then for the 3M cart first Part II Completely Inelastic Collisions Orient the two carts so their hook and pile ends are toward each other Make sure the plunger bar is pushed in completely so it won t interfere with the colli...

Page 15: ...nces Then the force is plotted versus distance and the slope of the result ing straight line is equal to k Procedure Measurements to Find the Theoretical Period Use the balance to find the mass of the cart Record this value at the top of Table 3 1 Level the track by setting the cart on the track to see which way it rolls Adjust the leveling feet at the ends of the track to raise or lower the ends ...

Page 16: ...his data in Table 3 2 Calculations Theoretical Period Using the data in Table 3 1 plot force versus displacement Draw the best fit straight line through the data points and determine the slope of the line The slope is equal to the effec tive spring constant k k ______________ Using the mass of the cart and the spring constant calculate the period using the theoretical formula Also calculate the th...

Page 17: ...rence between the measured and theoretical values cart alone diff ________________ cart with mass diff ________________ Questions Does the period of oscillation increase or decrease as the mass is increased Does a more massive cart oscillate faster or slower If the initial displacement from equilibrium amplitude is changed does the period of oscilla tion change Try it Table 3 2 Trial Time for 5 Os...

Page 18: ...14 Dynamics Cart Accessory Track Set 012 05035E Notes ...

Page 19: ...applying different forces to stretch the spring different distances When the force is plotted versus distance the slope of the resulting straight line is equal to k Procedure Measurements to Find the Theoretical Period Use the balance to find the mass of the cart Record this value at the top of Table 4 1 Set the cart on the track and attach a spring to one end of the cart by inserting the end of t...

Page 20: ...eps 6 and 7 Calculations Theoretical Period Using the data in Table 4 1 calculate the force caused by the additional mass in the cart F mg sinθ where θ is the angle of incline Plot force versus displacement Draw the best fit straight line through the data points and determine the slope of the line The slope is equal to the effective spring constant k k ______________ Using the mass of the cart and...

Page 21: ...e for 3 oscillations Calculate the period by dividing these times by 3 and record the periods in Table 4 2 Questions Does the period vary as the angle is changed How do the experimental values compare with the theoretical values Does the equilibrium position change as the angle is changed What would be the period if the angle was 90 degrees Time for 3 oscillations ...

Page 22: ...18 Dynamics Cart Accessory Track Set 012 05035E Notes ...

Page 23: ... T2 When two springs are combined in series or in parallel the spring constants add in different ways One possible way to add two spring constants is keffective k k 2k Another way is keffective 1 k 1 k 2 k which means that keffective 1 2 k Procedure Measuring k For a Single Spring Use the balance to find the mass of the cart Record this value at the top of Table 5 1 Set the cart on the track and a...

Page 24: ...using the same initial displacement amplitude Measuring the Effective k For Pairs of Springs Add a second spring in series as shown in Figure 5 2 and repeat Step Put the two springs in parallel as shown in Figure 5 3 and repeat Step Arrange the springs as shown in Figure 5 4 and repeat Step Figure 5 1 Equipment Setup Figure 5 2 Springs in Series Figure 5 4 Final Spring Arrangement Figure 5 3 Sprin...

Page 25: ...he periods in Table 5 1 Using the periods and the mass of the cart calculate the effective spring constants Mass of Cart ______________ Questions Is keffective 2k for springs in series or parallel Is keffective k for springs in series or parallel Is the last spring arrangement series or parallel Time for 2 oscillations Springs Trial 1 2 3 4 5 Avg Period k One Series Parallel At Ends Table 5 1 1 2 ...

Page 26: ...on the cart with a ruler Observe the resulting acceleration This will be a qualitative measurement VARY THE FORCE Perform the first trial with the spring plunger cocked to the first possible position the least compression and then do two more trials increasing the force applied to the cart by increasing the compression of the spring plunger VARY THE MASS For these trials always cock the spring plu...

Page 27: ...qual to m1 m2 a when friction is ignored To obtain the acceleration the cart will be started from rest and the time t it takes for it to travel a certain distance d will be measured Then since d 1 2 at2 the acceleration can be calculated using a 2d t2 assuming a constant Procedure Level the track by setting the cart on the track to see which way it rolls Adjust the leveling feet to raise or lower ...

Page 28: ... record in Table 7 1 Calculate the total distance traveled by taking the difference between the initial and final positions of the cart as given in Table 7 1 Calculate the accelerations and record in Table 7 2 For each case calculate the total mass multiplied by the acceleration and record in Table 7 2 For each case calculate the net force acting on the system and record in Table 7 2 Calculate the...

Page 29: ...red Then since d 1 2 at2 the acceleration can be calculated using a 2d t2 Then a plot of acceleration versus sinθ should give a straight line with a slope equal to the acceleration due to gravity g Procedure Set up the track as shown in Figure 8 2 raising the end of the track without an end stop about 10 cm Set the cart on the track against the end stop and record this final position of the cart a...

Page 30: ...rt _______________ Final Position of Cart _______________ Total distance d _______________ Data Analysis Calculate the average time for each angle Calculate the total distance traveled by taking the difference between the initial and final positions of the cart as given at the top of Table 8 1 Calculate the accelerations using the distance and times and record in Table 8 2 Measure the hypotenuse o...

Page 31: ...e best fit straight line and calculate its slope This slope should equal g Calculate the percent difference between the slope and g slope ______________________ difference _______________ Questions Does your reaction time cause a greater percentage error for higher or lower angles If the mass of the cart is doubled how are the results affected Try it ...

Page 32: ...28 Dynamics Cart Accessory Track Set 012 05035E Notes ...

Page 33: ...the resulting straight line is equal to k The gravitational potential energy gained by a cart as it climbs an incline is given by potential energy mgh where m is the mass of the cart g is the acceleration due to gravity and h is the vertical height the cart is raised In terms of the distance d along the incline the height is given by h d sinθ If energy is conserved the potential energy in the comp...

Page 34: ...l Energy Remove the leveling feet Remove the string from the cart and cock the spring plunger to its maximum compression position Place the cart against the end stop Measure the distance the spring plunger is compressed and record this value in Table 9 2 Incline the track and measure its height and hypotenuse see Figure 9 2 to determine the angle of the track angle arc sin Record the angle in Tabl...

Page 35: ...isplacement Draw the best fit straight line through the data points and determine the slope of the line The slope is equal to the effective spring constant k k ______________ Calculate the spring potential energy and record in Table 9 3 Calculate the gravitational potential energy for each case and record in Table 9 3 Calculate the percent difference between the spring potential energy and the gra...

Page 36: ...32 Dynamics Cart Accessory Track Set 012 05035E Notes ...

Page 37: ...n initially and observe Add a mass bar to one cart and repeat Experiment 13 Newton s Second Law III Repeat Experiment 7 with the track inclined so the pulley is on the high end and the cart accelerates up the incline Experiment 14 Damped Motion Incline the track with the end stop at the bottom Release the cart from a measured distance up the inclined track The spring plunger should be unlocked and...

Page 38: ...part Push the left cart into the middle cart which in turn will collide with the right cart The carts will all stick together Note the resulting final velocity of the carts Experiment 19 Rocket Staging Use three or more Dynamics Carts with plungers to simulate a rocket expelling fuel Push the plungers in on each cart and attach the carts together in a line on the 7 5 track Tape can be used to ligh...

Page 39: ...tum transfer will be proportional to the ratio of the cart masses Notes on Data Analysis M1 M2 Position X1 X2 X1 X2 M2 M1 497 5 500 7 181 0 42 0 41 5 1 01 1 01 497 5 996 4 195 0 56 0 27 5 2 04 2 00 497 5 1494 9 201 5 62 5 21 0 2 98 3 00 995 7 1494 9 189 0 50 0 33 5 1 49 1 50 Answers to Questions Momentum is conserved in each case As shown in this lab the momentum of each cart is the same KE2 m1 m2...

Page 40: ...s value will vary from spring to spring Theoretical values will vary depending on the value for k and for m For best results measure the carts rather than assume their weight to be the stated 500g Notes on Comparison The percent difference between experimental and theoretical values should be less than 2 and it is not unusual to obtain errors of less than 0 5 Notes on Questions The period of oscil...

Page 41: ... contribution due to friction changes with angle as well The experimental results should agree with theory to within 2 although it is not unusual to find agreement within less than 1 The equilibrium position changes as the angle is changed The period would be the same at 90 as long as the spring was not overstretched NOTE hanging the PASCO dynamics cart from the spring supplied with this equipment...

Page 42: ...ff the end of the track when the springs are in series Notes on Calculations The two springs used for this experiment had spring constants of 1 53 and 1 60 In series the spring constant was 0 76 k 2 In parallel the spring constant was 3 12 2k The spring constant was 3 06 2k when the springs were attached to the ends of the cart Notes on Questions Experiment 6 Newton s Second Law This lab is intend...

Page 43: ...fference be tween the two is the force of friction The hanging mass is accelerating at the same rate as the cart so its mass must be considered as well as that of the cart The cart is on a level track so it is not accelerated by gravity Experiment 8 Acceleration Down an Incline Data Analysis 0 0 2 0 4 0 6 0 8 1 1 2 1 4 0 0 02 0 04 0 06 0 08 0 1 0 12 0 14 Acceleration m s s Sin angle f x 9 476749E ...

Page 44: ...8 11 07 0 4971 19 5 0 0374 0 1824 5 66 11 07 0 9926 10 1 0 0194 0 1886 2 43 3 026 0 9926 39 0 0 0206 0 2003 3 58 3 026 0 4971 75 1 0 0396 0 1931 0 11 Notes on Questions The initial spring potential energy is larger Gener ally There are experimental errors which can make the gravitational energy appear larger than the initial spring potential The lost energy goes into friction Why not The increased...

Page 45: ...acting Technical Support Before you call the PASCO Technical Support staff it would be helpful to prepare the following information If your problem is with the PASCO apparatus note Title and model number usually listed on the label Approximate age of apparatus A detailed description of the problem sequence of events in case you can t call PASCO right away you won t lose valuable data If possible h...

Page 46: ......

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